anger, because of something that is wrong or not fair
a feeling of being upset or annoyed, usually because you feel that someone has been rude or shown no respect to you
Definitions from Cambridge dictionary.
The distinction between them seems to be that umbrage can be used when something actually offensive or unjust is done to arouse anger, while indignation would be used only when there is a perception of injustice.
I want to know if the two words have the same connotation.